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Mirrors > Home > NFE Home > Th. List > pw1ss | Unicode version |
Description: Unit power set preserves subset. (Contributed by SF, 3-Feb-2015.) |
Ref | Expression |
---|---|
pw1ss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspwb 4118 |
. . 3
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2 | ssrin 3480 |
. . 3
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3 | 1, 2 | sylbi 187 |
. 2
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4 | df-pw1 4137 |
. 2
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5 | df-pw1 4137 |
. 2
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6 | 3, 4, 5 | 3sstr4g 3312 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-pw 3724 df-sn 3741 df-pw1 4137 |
This theorem is referenced by: sspw1 4335 |
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